Physics 6820 -- General Relativity

This course is an introduction to general relativity, aimed at advanced undergraduates and beginning graduate students. Standard undergraduate coursework (including mechanics, special relativity, multivariable calculus, and linear algebra) will be assumed as background. I will not assume you have had any prior exposure to tensor calculus or curved manifolds; the first part of the course will introduce this material.

The course will meet Wednesdays and Fridays, 12:40-2:45 PM, in Smith Lab 1094. The first class will be held on Wednesday, August 21.

The main course text will be Bernard Schutz, A First Course in General Relativity.

Topics covered will include the following: (note I changed the ordering to follow the book)

• Overview; perspectives on GR
• Special relativity
• Coordinate systems, vectors, up and down indices, tensors
• Stress-energy tensor
• Tensors, geodesics, and calculus on curved manifolds
• The postulates of general relativity and Einstein's equations
• Weak field gravity -- gravitational redshift and the deflection of light
• Gravitational waves
• Compact stars, black holes, gravitational collapse, and the event horizon
• The expanding Universe -- the Friedmann equations and dark energy

Announcements

• Class will be shortened on Wednesday, September 25 (end at 1:50 PM). CCAPP postdoc Ami Choi will teach the Friday, September 27 class at the usual time.

Procedures

Homeworks will be due on Fridays. Office hours will be held on Thursdays, 11-12 and 4-5, in PRB M2010 (starting Aug. 30).

There will be an in-class midterms (1 hour) and a final exam. Please contact the professor if you require alternate arrangements for either or both exams.

• The mid-term exam will be on Wednesday, October 9 from 12:40-1:40 PM in Smith Lab 1094.
  • The mid-term will be open notes (including your notes from the course, and my lecture notes).
  • The exam duration will be 1 hour.
  • There will be 1 problem on the midterm. You will get a metric and be asked to do some standard calculations with it. The problem will not require any specialized prior knowledge -- the methods we have covered in class will suffice.
• The final exam will be on Monday, December 9 from 4:00-5:45 PM in Smith Lab 1094.

Grading will be based on the homework (75%), midterm (10%), and final (15%).

Lectures

(Corrections are marked in red.)

1. Lecture 1 - A review of special relativity
2. Lecture 2 - Examples from special relativity
3. Lecture 3 - Vector algebra in special relativity
4. Lecture 4 - Particle motion in special relativity [corrected Eq. (9)]
5. Lecture 5 - Tensor algebra in flat spacetime [corrected Eq. (23)]
6. Lecture 6 - Tensor calculus in flat spacetime
7. Lecture 7 - Particles, fluids, and the stress-energy tensor
8. Lecture 8 - Algebra and calculus with curved coordinate systems [corrected Eqs. (32,33,40)]
9. Lecture 9 - Geodesics and parallel transport
10. Lecture 10 - Curvature
11. Lecture 11 - The Einstein field equation
12. Lecture 12 - Gravitational lensing in the weak-field regime
13. Lecture 13 - Gravitational waves: generation and propagation
14. Lecture 14 - Gravitational waves: energy and evolution of binary systems [minor typo corrected]
15. Lecture 15 - Gravitational waves: astrophysical sources and detection
    • Slides: [ PPTX || PDF ]
16. Lecture 16 - Spherically symmetric stars [corrected Eqs. (35), (45), (46)]
17. Lecture 17 - Geodesics in the Schwarzschild geometry [typo corrected for r/M of Earth orbiting Sun]
18. Lecture 18 - The nature of the event horizon
19. Lecture 19 - Angular momentum and rotating black holes
20. Lecture 20 - The area theorem
21. Lecture 21 - Hawking radiation
22. Lecture 22 - The homogeneous, isotropic Universe
23. Lecture 23 - Evolution of the Universe

Homework

1. Homework 1 (due Friday, August 30) [Solutions]
2. Homework 2 (due Friday, September 6) [Solutions]
3. Homework 3 (due Friday, September 13; corrected) [Solutions]
4. Homework 4 (due Friday, September 20) [Solutions]
5. No homework due Friday, September 27
6. Homework 5 (due Friday, October 4) [Solutions]
7. No homework due Friday, October 11 or October 18
8. Homework 6 (due Friday, October 25) [Solutions]
9. No homework due Friday, November 1
10. Homework 7 (due Friday, November 8) [Solutions]
11. No homework due Friday, November 15
12. Homework 8 (due Friday, November 22) [Solutions]
    • HW8 is the last homework!

Exam solutions

[ Midterm || Final ]